Abstract
In this chapter we present initial characteristic results of our term structure model. At first, we show how to price discount bonds considered to be the most basic interest rate contracts serving as pure securities in the sense of Arrow/Debreu. Based on the discount bond pricing formula we are able to derive the term structures of interest rates and volatilities. Further, we analyze limiting cases of our model where we first demonstrate that our model contains the Ornstein-Uhlenbeck process model proposed by Vasicek (1977) as special case. Second, we examine the asymptotic behavior of the term structure of spot interest rates at the short and long end. In the last section we discuss the core influences of the state variables and the model parameters on the shape of the term structures in a comparative statistic analysis. Such an analysis is considered relevant in order to know which type of term structures are realizable within the model and to get an idea on how changes in the values of the state variables and the model parameters influence the shape of the term structures.
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As we discuss in section 13.3.1, to get a solution for Ai = 0 we need to go back to the original system of partial differential equations of (13.3) to (13.5).
This equivalently is the determinant of the system matrix.
For a better understanding of the independent variables of the functions A(t) and B(t) we add the parameter T to the final expressions, i.e. denote the functions as A (t, T) and B (t,T).
This alternative derivation is of interest in terms of studying the equilibrium behavior of the system, because it nicely relates to the nonhomogeneous partial differential equation which is known from physics to model oscillation. However, our approach is more symmetric in its formulation and derivation of the solutions to A (t) and B (t).
We also add the parameter T to the final expression on the function C (t) for a better understanding, i.e. we denote the function as C (t,T).
See equation (13.21).
The empirical parameter estimates will be considered in depth in chapter 15 on the calibration of the model to US interest rate data.
The empirical mean values are those obtained for the US Treasury data set shown in table 15.7 on page 168.
See the empirical results shown in table 15.7 on page 168.
See the results given in table 15.6 on page 163.
The long-run means of the state variables in the data set are x l = [0.0950, —0.1311]′ which are based on the US interest data; for further analysis of the state variables see section 15.3.3.
Compare the results presented on the empirical estimations in chapter 15.
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© 2001 Springer-Verlag Berlin Heidelberg
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Kellerhals, B.P. (2001). Initial Characteristic Results. In: Financial Pricing Models in Continuous Time and Kalman Filtering. Lecture Notes in Economics and Mathematical Systems, vol 506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21901-0_13
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DOI: https://doi.org/10.1007/978-3-662-21901-0_13
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